Rahane and opening partner Shane Watson (31) set the tone with a 62-run stand in 7.2 overs after the Royals chose to bat first.

Number three Dishant Yagnik also chipped in with 34 and Brad Hodge (25no) launched a couple of late sixes to see Rajasthan up to 179-3.

And that proved plenty as the Indians quickly slumped to 31-4 in reply with off-spinner Ajit Chandila (2-6) accounting for Sachin Tendulkar (1) and Ricky Ponting (4) in his first two overs.

Dinesh Karthik (30) and Ambati Rayudu (27) were the only contributors of note as Mumbai were all out for 92 from the second ball of the 19th over. Rajasthan's Australian left-arm seamer James Faulkner finished with 3-16.

The result moves Rajasthan top of the IPL table, level on eight points with Royal Challengers Bangalore and Sunrisers Hyderabad but having played a game less.